3 d}e@srdZddlZddlZddlZddlZddlmZddlmZddl m Z m Z m Z m Z mZmZmZmZmZmZmZmZmZmZmZGdddeZGdd d eZd d Zd d ZddZddZGddde Z!ej"dZ#ej"dZ$ej"dej%Z&ddZ'd.ddZ(Gddde Z)GdddZ*dZ+d/d d!Z,d0d#d$Z-d1d%d&Z.d2d'd(Z/d3d)d*Z0e1d+krne0d,dd-dS)4zK This module provides data structures for representing first-order models. N)pformat) decorator)AbstractVariableExpression AllExpression AndExpressionApplicationExpressionEqualityExpressionExistsExpression Expression IffExpression ImpExpressionIndividualVariableExpressionLambdaExpressionNegatedExpression OrExpressionVariable is_indvarc@s eZdZdS)ErrorN)__name__ __module__ __qualname__rr1/tmp/pip-build-v9q4h5k9/nltk/nltk/sem/evaluate.pyr+src@s eZdZdS) UndefinedN)rrrrrrrr/srcOsVtj|}tt|d|}|jddrLtx|jD]}td|q8W|||S)Nrtracez%s => %s)inspectZgetfullargspecdictzippopprintitems)fargskwZargspecditemrrrr3s  rcCsNt|dkrdStdd|Dr>tt|tt|kr>dStd|dS)z Check whether a set represents a relation (of any arity). :param s: a set containing tuples of str elements :type s: set :rtype: bool rTcss|]}t|tVqdS)N) isinstancetuple).0elrrr Iszis_rel..z.Set %r contains sequences of different lengthsN)lenallmaxmin ValueError)srrris_rel=s *r1cCsTt}xH|D]@}t|tr(|j|fq t|trB|jt|q |j|q W|S)aR Convert a set containing individuals (strings or numbers) into a set of unary tuples. Any tuples of strings already in the set are passed through unchanged. For example: - set(['a', 'b']) => set([('a',), ('b',)]) - set([3, 27]) => set([('3',), ('27',)]) :type s: set :rtype: set of tuple of str )setr&straddint)r0newelemrrrset2relOs    r8cCs t|dkrdStt|dS)ze Check the arity of a relation. :type rel: set of tuples :rtype: int of tuple of str r)r+list)relrrraritygs r;csTeZdZdZfddZddZddZedd Zed d Z e d d Z Z S) Valuationa A dictionary which represents a model-theoretic Valuation of non-logical constants. Keys are strings representing the constants to be interpreted, and values correspond to individuals (represented as strings) and n-ary relations (represented as sets of tuples of strings). An instance of ``Valuation`` will raise a KeyError exception (i.e., just behave like a standard dictionary) if indexed with an expression that is not in its list of symbols. csttjxd|D]\\}}t|ts,t|tr6|||<qt|trNt|||<qtjd||fdd}t |qWdS)z= :param xs: a list of (symbol, value) pairs. zGError in initializing Valuation. Unrecognized value for symbol '%s': %sB)widthN) super__init__r&r3boolr2r8textwrapfillr/)selfxssymvalmsg) __class__rrr@~s   zValuation.__init__cCs$||krtj||Std|dS)NzUnknown expression: '%s')r __getitem__r)rDkeyrrrrJs zValuation.__getitem__cCst|S)N)r)rDrrr__str__szValuation.__str__cCsRg}xD|jD]8}t|tr(|j|qt|ts|jdd|DqWt|S)z7Set-theoretic domain of the value-space of a Valuation.cSs"g|]}|D]}|dk r |q qS)Nr)r(tuple_r7rrr sz$Valuation.domain..)valuesr&r3appendrAextendr2)rDdomrGrrrdomains   zValuation.domaincCs t|jS)z9The non-logical constants which the Valuation recognizes.)sortedkeys)rDrrrsymbolsszValuation.symbolscCst|S)N)read_valuation)clsr0rrr fromstringszValuation.fromstring) rrr__doc__r@rJrLpropertyrSrV classmethodrY __classcell__rr)rIrr<rs   r<z \s*=+>\s*z\s*,\s*zg\s* (\([^)]+\)) # tuple-expression \s*cCstj|}|d}|d}|jdr|dd}tj|}|rvg}x<|D](}|dd}ttj|}|j|qHWn tj|}t|}||fS)a Read a line in a valuation file. Lines are expected to be of the form:: noosa => n girl => {g1, g2} chase => {(b1, g1), (b2, g1), (g1, d1), (g2, d2)} :param s: input line :type s: str :return: a pair (symbol, value) :rtype: tuple r{r`) _VAL_SPLIT_REsplit startswith _TUPLES_REfindallr'_ELEMENT_SPLIT_RErPr2)r0piecessymbolvalueZ tuple_stringsZ set_elementstselementrrr_read_valuation_lines       rlcCs|dk r|j|}g}xt|jD]p\}}|j}|jds$|dkrHq$y|jt|Wq$tk r}ztd|d||WYdd}~Xq$Xq$Wt|S)a Convert a valuation string into a valuation. :param s: a valuation string :type s: str :param encoding: the encoding of the input string, if it is binary :type encoding: str :return: a ``nltk.sem`` valuation :rtype: Valuation N#zUnable to parse line z: ) decode enumerate splitlinesstriprcrPrlr/r<)r0encodingZ statementslinenumlineerrrrWs  ,rWcsTeZdZdZdfdd ZddZddZdd d Zd d Zd dZ ddZ Z S) Assignmentae A dictionary which represents an assignment of values to variables. An assignment can only assign values from its domain. If an unknown expression *a* is passed to a model *M*\ 's interpretation function *i*, *i* will first check whether *M*\ 's valuation assigns an interpretation to *a* as a constant, and if this fails, *i* will delegate the interpretation of *a* to *g*. *g* only assigns values to individual variables (i.e., members of the class ``IndividualVariableExpression`` in the ``logic`` module. If a variable is not assigned a value by *g*, it will raise an ``Undefined`` exception. A variable *Assignment* is a mapping from individual variables to entities in the domain. Individual variables are usually indicated with the letters ``'x'``, ``'y'``, ``'w'`` and ``'z'``, optionally followed by an integer (e.g., ``'x0'``, ``'y332'``). Assignments are created using the ``Assignment`` constructor, which also takes the domain as a parameter. >>> from nltk.sem.evaluate import Assignment >>> dom = set(['u1', 'u2', 'u3', 'u4']) >>> g3 = Assignment(dom, [('x', 'u1'), ('y', 'u2')]) >>> g3 == {'x': 'u1', 'y': 'u2'} True There is also a ``print`` format for assignments which uses a notation closer to that in logic textbooks: >>> print(g3) g[u1/x][u2/y] It is also possible to update an assignment using the ``add`` method: >>> dom = set(['u1', 'u2', 'u3', 'u4']) >>> g4 = Assignment(dom) >>> g4.add('x', 'u1') {'x': 'u1'} With no arguments, ``purge()`` is equivalent to ``clear()`` on a dictionary: >>> g4.purge() >>> g4 {} :param domain: the domain of discourse :type domain: set :param assign: a list of (varname, value) associations :type assign: list Ncsptj||_|r^xH|D]@\}}||jks>tdj||jt|sRtd||||<qWd|_|jdS)Nz'{}' is not in the domain: {}z-Wrong format for an Individual Variable: '%s')r?r@rSAssertionErrorformatrvariant _addvariant)rDrSZassignvarrG)rIrrr@/s     zAssignment.__init__cCs$||krtj||Std|dS)Nz"Not recognized as a variable: '%s')rrJr)rDrKrrrrJ?s zAssignment.__getitem__cCst|j}|j||S)N)rwrSupdate)rDr6rrrcopyEs  zAssignment.copycCs |r ||=n|j|jdS)z Remove one or all keys (i.e. logic variables) from an assignment, and update ``self.variant``. :param var: a Variable acting as a key for the assignment. N)clearr{)rDr|rrrpurgeJs zAssignment.purgecCs:d}t|j}x&|D]\}}|d|d|d7}qW|S)zQ Pretty printing for assignments. {'x', 'u'} appears as 'g[u/x]' g[/])rTrz)rDZgstringrzrGr|rrrrLXs  zAssignment.__str__cCs:g}x*|jD]}|d|df}|j|qW||_dS)zK Create a more pretty-printable version of the assignment. r^rN)r rPrz)rDlist_r%pairrrrr{cs zAssignment._addvariantcCsF||jkst|d|jt|s2td||||<|j|S)zh Add a new variable-value pair to the assignment, and update ``self.variant``. z is not in the domain z-Wrong format for an Individual Variable: '%s')rSrxrr{)rDr|rGrrrr4ns zAssignment.add)N)N) rrrrZr@rJr~rrLr{r4r]rr)rIrrws3   rwc@sPeZdZdZddZddZddZdd d Zdd d ZdddZ dddZ dS)Modela[ A first order model is a domain *D* of discourse and a valuation *V*. A domain *D* is a set, and a valuation *V* is a map that associates expressions with values in the model. The domain of *V* should be a subset of *D*. Construct a new ``Model``. :type domain: set :param domain: A set of entities representing the domain of discourse of the model. :type valuation: Valuation :param valuation: the valuation of the model. :param prop: If this is set, then we are building a propositional model and don't require the domain of *V* to be subset of *D*. cCs<t|tst||_||_|j|js8td|j|fdS)NzDThe valuation domain, %s, must be a subset of the model's domain, %s)r&r2rxrS valuation issupersetr)rDrSrrrrr@s zModel.__init__cCsd|jd|jdS)N(z, ))rSr)rDrrr__repr__szModel.__repr__cCsd|jd|jS)Nz Domain = z, Valuation = )rSr)rDrrrrLsz Model.__str__Nc CszyBtj|}|j|||d}|r@ttd|d|d||Stk rt|rpttd|d|dSXdS)aA Read input expressions, and provide a handler for ``satisfy`` that blocks further propagation of the ``Undefined`` error. :param expr: An ``Expression`` of ``logic``. :type g: Assignment :param g: an assignment to individual variables. :rtype: bool or 'Undefined' )r'z' evaluates to z under M, z' is undefined under M, rN)r rYsatisfyrr)rDexprrrparsedrirrrevaluates  zModel.evaluatecsPt|trt|j\}}t|trLj|}tfdd|D}||kSj|j}j|j}||Snt|trj|j  St|t rj|j oj|j St|t rڈj|j p؈j|j St|trj|j  pj|j St|tr.j|j j|j kSt|trVj|j j|j kSt|trj} x4jD]*} | j|jj| j|j | srdSqrWdSt|trj} x4jD]*} | j|jj| j|j | rdSqWdSt|tr>i} |jj} x.jD]$} j|j j| | } | | | <qW| Sj||SdS)a Recursive interpretation function for a formula of first-order logic. Raises an ``Undefined`` error when ``parsed`` is an atomic string but is not a symbol or an individual variable. :return: Returns a truth value or ``Undefined`` if ``parsed`` is complex, and calls the interpretation function ``i`` if ``parsed`` is atomic. :param parsed: An expression of ``logic``. :type g: Assignment :param g: an assignment to individual variables. c3s|]}j|VqdS)N)r)r(arg)rrDrrr*sz Model.satisfy..FTN)r&rZuncurryrrr'functionZargumentrZtermrfirstsecondrr r rrr~rSr4variablenamer ri)rDrrrrZ argumentsfunvalZargvalsZargvalnew_guZcfr|rGr)rrDrrsV                    z Model.satisfyFcCsD|jj|jjkr|j|jjSt|tr4||jjStd|dS)a An interpretation function. Assuming that ``parsed`` is atomic: - if ``parsed`` is a non-logical constant, calls the valuation *V* - else if ``parsed`` is an individual variable, calls assignment *g* - else returns ``Undefined``. :param parsed: an ``Expression`` of ``logic``. :type g: Assignment :param g: an assignment to individual variables. :return: a semantic value zCan't find a value for %sN)rrrrVr&r r)rDrrrrrrrs   zModel.irc Cs>d}|||}g}t|tr(t|} n|} | |jkr&|r`tt||d|d|x|jD]} |j} | j| j| |r|dkr|d} nd} |j || | } |rt|d| | dkr|rt|d|d | d qh|j | |rht|d|d | d | qhWd d |D}nt | jd||S)a Generate the entities from the model's domain that satisfy an open formula. :param parsed: an open formula :type parsed: Expression :param varex: the relevant free individual variable in ``parsed``. :type varex: VariableExpression or str :param g: a variable assignment :type g: Assignment :return: a set of the entities that satisfy ``parsed``. z zOpen formula is 'z' with assignment r^rz(trying assignment %s)Fz value of 'z' under z is Falsez is cSsh|]}|qSrr)r(crrr Fsz#Model.satisfiers..z is not free in ) r&r3rfreerrSr~r4rrrPr)rDrZvarexrrZnestingZspacerindent candidatesr|rrZlowtraceriresultrrr satisfierss<        "zModel.satisfiers)N)N)F)Nr) rrrrZr@rrLrrrrrrrrr{s   E rcCstddd gatatttattattdt tdtdt tdttd ttdt d d d d dddddddddddddg}xB|D]:}|rttj |t|qtd|dtj |tqWdS)!z!Example of a propositional model.PTQRF*zPropositional Formulas Demoz7(Propositional constants treated as nullary predicates)z Model m1: z(P & Q)z(P & R)z- Pz- Rz- - Pz - (P & R)z(P | R)z(R | P)z(R | R)z (- P | R)z (P | - P)z(P -> Q)z(P -> R)z(R -> P)z (P <-> P)z (R <-> R)z (P <-> R)zThe value of 'z' is: N)rT)rT)rF) r<Zval1r2Zdom1rm1rwg1rmultr)rZ sentencessentrrrpropdemoVsD      rFc Csd"d#d$dddhfd dd hfd dhfd d%d&d'd(hfgattatjatttattd)d*ga|st t dt t dt dt t dd+dtt dtdd d dd ddg}dd|D}t xL|D]D}yt d|tj |tfWqt k r t d|YqXqWd,d.d0d2g}x|D]z\}}yDtj t j|t}tdd|D} t |d|d| |kWn*t k rt |d|d YnXq$Wd!S)3zExample of a first-order model.adamb1bettyrfidod1Zgirlg2boyb2Zdoglovexyrz Models Demoz Model m2: - zVariable assignment = walkszcSsg|]}tj|qSr)r rY)r(rvrrrrNszfolmodel..z&The interpretation of '%s' in m2 is %sz-The interpretation of '%s' in m2 is Undefinedcss |]}tjtj|tVqdS)N)m2rr rYr)r(rrrrr*szfolmodel..rz) evaluates to z) evaluates to UndefinedN)rr)rr)rr)rr)rr)rr)rr)rr)rrz--------------)rrr)rrrr)rrrr)rr)Zv2r<Zval2rSZdom2rrrwrrrrrr rYr') quietrexprsZ parsed_exprsrZ applicationsZfunr"rZargsvalrrrfolmodelsN        rcCstddttdttdtdtddddd d d d d dddddddddg}xD|D]<}tj|r~tj|t|q^td|dtj|tq^WdS)zF Interpretation of closed expressions in a first-order model. T)rrzFOL Formulas Demozlove (adam, betty)z (adam = mia)z\x. (boy(x) | girl(x))z\x. boy(x)(adam)z\x y. love(x, y)z\x y. love(x, y)(adam)(betty)z\x y. love(x, y)(adam, betty)z\x y. (boy(x) & love(x, y))z#\x. exists y. (boy(x) & love(x, y))zexists z1. boy(z1)z!exists x. (boy(x) & -(x = adam))z&exists x. (boy(x) & all y. love(y, x))zall x. (boy(x) | girl(x))z1all x. (girl(x) -> exists y. boy(y) & love(x, y))z3exists x. (boy(x) & all y. (girl(y) -> love(y, x)))z3exists x. (boy(x) & all y. (girl(y) -> love(x, y)))zall x. (dog(x) -> - girl(x))z-exists x. exists y. (love(x, y) & love(x, y))zThe value of 'z' is: N)rrrrrrr)rformulasfmlarrrfoldemos8    rcCsttdttdtdttddddddd d d d d ddddddddd dg}|rfttx|D]}t|tj|qlWdd|D}x0|D](}tjtdj|tj |dt|qWdS)z5Satisfiers of an open formula in a first order model.rzSatisfiers DemoT)rzboy(x)z(x = x)z(boy(x) | girl(x))z(boy(x) & girl(x))z love(adam, x)z love(x, adam)z -(x = adam)zexists z22. love(x, z22)zexists y. love(y, x)zall y. (girl(y) -> love(x, y))zall y. (girl(y) -> love(y, x))z)all y. (girl(y) -> (boy(x) & love(y, x)))z)(boy(x) & all y. (girl(y) -> love(x, y)))z)(boy(x) & all y. (girl(y) -> love(y, x)))z+(boy(x) & exists y. (girl(y) & love(y, x)))z(girl(x) -> dog(x))zall y. (dog(y) -> (x = y))z&exists y. (love(adam, y) & love(y, x))cSsg|]}tj|qSr)r rY)r(rrrrrNszsatdemo..zThe satisfiers of '{}' are: {}rN) rrrrr rYrrryr)rrrrprrrsatdemosD     rc CsVttttd}y|||dWn0tk rPx|D]}|||dq6WYnXdS)aO Run exists demos. - num = 1: propositional logic demo - num = 2: first order model demo (only if trace is set) - num = 3: first order sentences demo - num = 4: satisfaction of open formulas demo - any other value: run all the demos :param trace: trace = 1, or trace = 2 for more verbose tracing )r^)rN)rrrrKeyError)numrZdemosrrrdemos  r__main__r)r)N)N)FN)N)N)rN)2rZrresysrBpprintrZnltk.decoratorsrZnltk.sem.logicrrrrrr r r r r rrrrr Exceptionrrrr1r8r;rr<compilerarfVERBOSErdrlrWrwrrrrrrrrrrrrsB  D  B  # X 1 < , 0